IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO.

6, JUNE 2007 1591

Groundwave Modeling and Simulation Strategies and

Path Loss Prediction Virtual Tools
Levent Sevgi, Senior Member, IEEE

Dedicated to the memory of a long-lasting collaboration with that may cause surface and/or elevated ducts, tunnels, etc. Since
Leopold B. Felsen there was no globally applicable propagation method, we then
focused on numerical propagators based on observable wave ob-
jects and their hybridization [3]–[5]. After that, we started to
Abstract—Reliable and accurate groundwave propagation path develop and design user-friendly virtual propagation prediction
loss prediction between a pair of transmitter/receiver necessitates a tools [6]–[11] most of which can be used as teaching aids in
good understanding of electromagnetic wave scattering in the pres- virtual propagation labs of various propagation lectures. We al-
ence of non-flat terrain and inhomogeneous atmosphere, and this is ways looked for effective tools which would give physical in-
one of the major issues in radio communication and radar systems sight and be useful at the same time. He used to believe that
design. A propagation engineer desires to have a numerical prop-
agator that calculates the radiowave path loss, without going into physics-based, problem-matched tools either analytical or nu-
details and/or having a deep knowledge of the propagation phe- merical, are really important in teaching electromagnetics to a
nomena, between any two points specified on a digital map of the computer-weaned generation of students, with access to the in-
area of interest. Since a generally applicable, all-purpose propaga- ternet and consequent globalization of information [12].
tion prediction method has not developed yet one has to understand Groundwave propagation studies began with analytically
validity and accuracy ranges, and the limitations of available pre-
diction models and tools; this certainly requires, to some extent, the solvable idealized models over a smooth spherical earth (ba-
physical insight of the propagation problem at hand. This article sically in two-dimensional (2-D) space), then had progressed
aims to summarize groundwave propagation modeling and numer- toward more “reality” through physics-based numerical algo-
ical simulation strategies, and to review some of the virtual tools, rithms, operating in the frequency and short-pulse time domain,
introduced recently. which took advantage of computational resources. An extensive
Index Terms—Analytical methods, atmospheric refractivity sequence of simulations for various terrain and atmospheric
effects, electromagnetic wave propagation, finite-difference time- refractivities, as well as different source-receiver arrangements
domain (FDTD), groundwaves, Matlab, method of moments
and operating frequencies, served to calibrate these algorithms
(MoM), mixed-path propagation, non-flat terrain modeling,
numerical methods, numerical simulator, parabolic equation one against the other, and established the range of problem pa-
method, ray-mode approximations, short pulse propagation, split- rameters for which each was more effective. As it is inevitably
step PE (SSPE), surface impedance, surface waves, transmission difficult to give a chronological and complete list of references
line matrix (TLM), virtual tools, wave scattering. for a topic like this, only a small subset is included here. Most of
the early analytical works may be found in [13]–[16], statistical
studies and models in [17], [18], the details of the parabolic
I. INTRODUCTION
equation (PE) propagator and related studies in [19], the method
N THIS overview of groundwave propagation, dedicated to
I the memory of Leopold Benno Felsen (Leo), a particular
class of groundwave propagation scenarios in the presence of
of moments (MoM) [20] based propagators in [21], [22], the
finite-difference time-domain (FDTD) and the transmission
line matrix (TLM) based propagators in [6], [7], [23], [24], and
surface irregularities and atmospheric refractivities is addressed. an extended summary of groundwave propagation modeling in
The aim of this article is to pay homage to a long-lasting col- [8]. Recent tutorial papers on rural outdoor propagation in [4]
laboration with Leo Felsen on the design of various numerical and [25] are also worthwhile to list.
virtual tools (VT) that can be used for both educational and re-
search purposes in the propagation society. Our collaboration II. THE PROBLEM
[1]–[12] started in 1988 when I joined his research group as a
Ph.D. student in Farmingdale Campus of New York Polytechnic Maxwell equations represent wave propagation in both
University. Initially, we investigated various modal approaches spatial and time domains in open regions. One needs to take
for wave propagation modeling in guiding and anti-guiding en- into account necessary boundary (BC) and source conditions
vironments with longitudinal and transverse variations [1], [2] if propagation through natural and/or artificial waveguiding
structures is of interest. Long and medium (rural), and short
Manuscript received March 28, 2006; revised October 30, 2006.
(urban) range groundwave propagation problems are very
The author is with the Electronics and Communication Engineering Depart- complex and challenging. For realistic propagation prediction,
ment, Dogus University, Faculty of Engineering, Acibadem, 34722 Kadikoy/Is- a theoretical model (mathematical representations) and its
tanbul, Turkey (e-mail: lsevgi@dogus.edu.tr). discrete (computer) implementation must include all relevant
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org. scattering components (e.g., multiple reflections and refrac-
Digital Object Identifier 10.1109/TAP.2007.897256 tions, edge/tip diffractions, surface and/or leaky waves, etc.)
0018-926X/$25.00 © 2007 IEEE
1592 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 6, JUNE 2007

Fig. 2. Modeling and simulation strategies for groundwave propagation in var-

Fig. 1. A typical groundwave propagation scenario; a 2-D vertical projection ious environments; analytical methods, numerical techniques and empirical ap-
(computer-generated longitudinal terrain profile) of a digital map between a proaches (GO: Geometric optic, GTD: Geometric theory of diffraction, TD:
transmitter-receiver pair (HF: high frequency, 3–30 MHz, VHF: very high fre- time-domain, SSPE: split-step Parabolic equation, IFD: implicit finite-differ-
quency, 30–300 MHz, MW: microwaves, typically above 500 MHz). ence, BPM: beam propagation method, PW: plane wave, TDWP: time-domain
wave propagator, TLM: transmission line matrix).

that account for path loss between any two points in a 3-D digi-
tally-parameterized environment. Moreover, the terrain profile, “earth-flattening” non-dimensional 2-D rectangular co-
vegetation, Earth’s curvature, atmospheric refractivity, and the ordinates [3], [4], [8], [25]. The Earth’s curvature under the
presence of other obstacles must also be considered. Although standard atmosphere condition can be included by using
hardware and software technology is well-advanced toward , where is the refractivity value at the surface and
this goal, it is hard to say that current simulation algorithms is the effective Earth’s radius. Extra
are adequate enough to deal with this problem. The modelers terms are also added to model various super or sub-refraction
are still away from satisfying these requirements directly in propagation cases in terms of refractivity , or modified refrac-
3-D digital environments, and hence, field strength predictions tivity
along with 2-D paths are still of interest.

A. A Generic Rural Propagation Scenario (1)

A generic 2-D projection scenario of the groundwave
with the height given in kilometers. is dimensionless, but
problem is pictured in Fig. 1. The mission in such a scenario
is measured in “ units” for convenience, and depends on the
may be to establish communication links between various
pressure (mbar), the absolute temperature and the
terminals, to monitor surface and/or air activity in a specified
partial pressure of water vapor (mbar) as [8]
region with different types of EM sensors, etc. Some character-
istics and requirements may be listed as follows:
• Low and Medium frequency (LF, MF) communication
(2)
systems do not suffer from Earth’s surface irregularities
(non-flat terrain, vegetation, etc.); essentially one needs
which is valid in Earth-troposphere waveguides and can be used
to know the distance between the transmitter and the
in ground wave propagation modeling. For the standard atmos-
receiver.
phere decreases by about 40 Nunit/km while increases
• Establishing a long range surface marine communication
by about 117 Nunit/km (although standard atmosphere defines
link requires to use the HF band as well as an understanding
exponentially decreasing refractive index, this could be approx-
of the multi-mixed path (i.e., ocean-island transition) prop-
imated as being linear for low altitudes). Sub-refraction (super-
agation (known as Millington) effects.
refraction) occurs when the rate of change in with respect to
• Alternatively, sky wave HF systems may be used for the
height (i.e., ) is less (more) than 40 Nunit/km.
same purpose (since waves between 3–30 MHz may be
trapped between Earth and Ionosphere depending take-off
III. MODELING STRATEGIES
angle (TOA) of the transmitter).
• One may want to use VHF signals for the establishment of Major groundwave propagation modeling and numerical
a link with, for example, a low altitude missile, or an attack simulation strategies (Fig. 2) vary from mathematical exact
helicopter that hides behind a hill, and needs connection representations for idealized geometries, to pure numerical
via diffraction. ones, from purely empirical ones, based on extensive path loss
• Line-of-sight (LOS) requirements play an important role measurements to hybrid techniques that combine two or more
when dealing with UHF frequencies and above. methods to extend their range of validity and accuracy. This
section summarizes some of them in chronological order.
B. Atmospheric Refractivity
Horizontal and/or vertical refractivity variations may cause A. Early Analytical Studies
surface and/or elevated duct formations in groundwave propa- Early efforts for determining field behavior in a guiding envi-
gation. For the relevant source , observation heights, the ronment were to express propagation characteristics in terms of
earth’s radius , which satisfy the inequal- progressing (ray-type) or oscillatory (mode type) constituents,
ities and , respectively, the from which rigorous analytical algorithms can be developed.
3-D problem in spherical coordinates can be approximated in Normal modes (NM) are the solution of strictly-separable wave
SEVGI: GROUNDWAVE MODELING AND SIMULATION STRATEGIES AND PATH LOSS PREDICTION VIRTUAL TOOLS 1593

equations. They are orthonormal wave functions with finite en- where
ergy and are tagged by distinct longitudinal propagation con-
stants. The mode concept can be extended to weakly non-sepa- (5)
rable environments with slowly varying longitudinal character-
is the free-space field strength at the distance , is the free-
istics. This gives rise to adiabatic modes (AM) [26], which are
space wavenumber, is the dipole moment, , and
the solutions of weakly non-separable wave equation, and in-
trinsic modes (IM) [1], [2], [27], [28], which, in turn, extend the (6)
AM concept. There are also analytical studies based on edge
and/or tip diffraction effects, surface waves, traveling waves, is the ground reflection coefficient for the vertical polarization.
etc., [29], [30]. Other parameters are
A chronological order of a variety of analytic models for
groundwave propagation has already been listed, and the ide- (7)
alized conditions under which they apply have been discussed
in [4], [8]. Among these, a special attention was given to the (8)
(ray-optical) plus (surface wave) model of Norton [31] and the
surface guided mode model of Wait [32]. Novel numerical al-
gorithms were also presented [3] which, for any specified set (9)
of problem parameters, is designed to dynamically home in on
the best hybridization of the Norton and Wait analytic models; Here, is the angular frequency, is the complex permittivity
as the observer moves parallel to the Earth’s surface, passing of the ground, and are the heights of the transmitter and
from the illuminated region (where the Norton model is effi- receiver, respectively. The surface wave attenuation function is
cient) through the LOS into the shadow region (where the Wait defined as
model is efficient), the algorithm determines where and how to
affect the transition. The mixed-path propagation problem (i.e.,
Millington effect [33]) was also investigated to handle land-sea (10)
transitions, especially at HF and VHF frequencies [34]–[36].
It should be noted that emerging HF and VHF communica-
tion and radar technologies, intelligent transportation systems, where is the complementary error function with the
or Digital Radio Mondiale (DRM) (www.drm.org) necessitate complex argument . The function introduces an attenu-
revisiting [10] and using these early analytical models for short ation which depends on the range, frequency and electrical pa-
to long-wave systems, endorsed by the ITU Recommendations rameters of the ground. At ranges of a few wavelengths from the
[37]–[39]. The ITU-R P-368-7 [37] fully covers both homoge- transmitter, has a value of nearly unity [(3), (4) are called
neous and mixed-path groundwave propagation problems, and non-attenuated surface wave at these ranges], and causes
gives a set of predicted field strength versus distance curves almost exponential decay at medium ranges and varies inversely
for the vertically polarized waves in the MF and HF bands for as the square of the distance from the transmitter.
variety of ground conductivity and relative permittivity 2) Wait’s Surface Wave Contribution: The Wait formulation
values. These curves are valid for a certain range of antenna restructures the spectral integral as a series of NM propagating
heights up to if , and for the along the earth’s surface. Wait expressed the attenuation func-
non-flat longitudinal paths with obstacles not higher than a tion in terms of height gain functions for the vertical (radial)
wavelength and not closer than 8–10 km either to the component of electric field [41] in flatted-Earth as
transmitter or receiver. The field strength prediction for digital
(11)
sound broadcasting systems is covered by ITU-R P-1321 [38]
and BS-1615 [39], and points out the usage of ITU-R P-368-7, with the same given in (5), and the attenuation function
for the groundwave field strength prediction in the MW band.
1) Norton’s Surface Wave Contribution: The Norton formu-
lation [31] extracts a ray-optical asymptotic approximation from
(12)
a wavenumber spectral integral representation, under the stan-
Here, is the refractive index at Earth’s surface and is the
dard (homogeneous) atmosphere assumption. Since the space
surface impedance given as
wave cancels out at long ranges (and/or when transmitter/re-
ceiver is on or close to the ground) it is sufficient to use Norton’s
expressions for the vertical and tangential electric field compo-
nents of the surface waves in the earth-flattening approximation
as (13)

(3) The transverse mode functions for the standard atmosphere with
inclusion of the Earth’s curvature are the well-known solutions
of the Airy equation
(4)
(14)
1594 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 6, JUNE 2007

which satisfy the impedance boundary condition on the surface for non-penetrable surfaces [22]. Moreover, the spectral acceler-
ation algorithms were proposed to overcome the computational
limitation of the FBM over slightly rough 1-D PEC surfaces.
(15)
C. Recent Time Domain Approaches
and the radiation condition at . Now, the wave phe- Time domain (TD) techniques such as the finite-difference
nomenology is modeled via transverse (x-domain) oscillatory time domain (FDTD) and the transmission line matrix (TLM)
modal fields, which progress with fixed wavenumber along have also been applied to realistic propagation problems [6], [8],
z. Only the radial component of the electric field excited by a [51]. The entire propagation domain can not be discretized in the
vertically polarized short dipole is given because the tangential FDTD or TLM scheme when long-range and/or high frequency
component is negligible in this formulation. The height propagation is of interest. One approach for modeling ground-
gain functions, i.e., the last two terms in (12), are convenient for wave propagation of localized wave objects through complex
parameterizing the effects of both transmit and receive antenna environment is to apply a sliding window technique. Since the
heights with respect to path loss variations. propagation (sliding) window traces a semi-open region, pow-
Norton-ray and Wait-mode formulations parameterize the erful signal processing techniques and free-space simulators are
propagation process in terms of different phenomenological essential for the success of the FDTD and TLM simulations.
models, and therefore their ranges of validity, accuracy, rate The two simulators introduced recently, TD wave propagator
of convergence, etc., depend on various parameters such as (TDWP) [6] and TLMWP [7], based on the FDTD and TLM, re-
operational frequency, source/observer locations, and physical spectively, have been validated and calibrated against analytical
propagation environment [3]. The ray-mode methods individ- exact as well as measurement results for a variety of different
ually, or their hybridization, can not handle problems such as groundwave propagation scenarios in 2-D [23]. Their extension
propagation over rough surface (non-flat) terrain or propagation to 3-D scenarios is quite straightforward, but requires massive
through surface and/or elevated ducts formed by inhomogeneous computer resources as well as parallel processing techniques.
vertical as well as horizontal atmospheric conditions [4], [8]. Hybrid methods that combine the asymptotic ray technique and
the FDTD have also been introduced, with alternative moving
B. Frequency Domain (FD) Methods window formulations for a pulsed, plane wave propagation in
various environments [24].
Groundwave propagation of general, source-excited wave
fields can be synthesized in terms of these building blocks
IV. CHARACTERISTIC EXAMPLES
(modes and rays) if available, and may serve as reference for the
validation, verification and calibration purposes. To go beyond A few characteristic examples related to the groundwave
into more realistic environments, one has to resort numerical propagation modeling and simulation studies are included in
modeling simulation approaches. Pioneering numerical mod- this section. The challenge is to predict groundwave path loss
eling studies are in FD, and one of the well-known methods is between any pair of transmitter/receiver via [37]
the parabolic equation (PE) [19], [40]–[43] (see [19] for details (16)
and all other related studies). The PE has been in use for many
decades, first applied in 2-D underwater acoustics and then in which requires the calculation of electric field strength at
EM and optics under various names (e.g., split-step PE (SSPE), the receiver at a distance . It should be noted that signal versus
implicit finite-difference PE (IFD-PE) and beam propagation range curves may be plotted in three different ways; path loss
method (BPM) as listed in Fig. 2). The PE techniques have been versus range using (16), propagation factor, defined as the field
improved to handle propagation effects over irregular terrain as strength in the presence of ground and atmospheric irregular-
well as lossy boundaries [19], [44]–[48]. The 3-D PE techniques, ities normalized to the free space field strength, versus range,
either in scalar or vector forms, have also been developed to or only field strength versus range. Note also that the spherical
study HF to microwave propagation for the last couple of years and cylindrical electromagnetic wave spread factors are and
[49], [50]. Today, PE-based tools have become essential for as- , respectively.
sessing clear-air and terrain effects on groundwave propagation.
Its applicability has been extended to regions where regular A. The Millington Mixed-Path Problem
PE does not work by including domain truncation, impedance The Millington curve fitting method described in ITU-R
boundaries and the implementation of fast hybrid methods P-368-7 [37] is an effective and quite accurate approach, but
combining ray-tracing and PE techniques [19]. unfortunately, its application by using the propagation curves
Wave scattering from irregular surfaces has also been treated given in the ITU-R P-368-7 is quite time consuming. Based
with the well-known MoM [8], based on integral equation for- on the previous mixed path calculator (which we developed
mulations (see the special issue [21] for the review of MoM- with Leo Felsen [3]) that uses the hybridization of Norton-Wait
based propagation modeling approaches). The primary factor formulations, a new VT which calculates groundwave field
limiting the use of MoM-based propagators in the calculation of strength values over smooth, spherical, lossy Earth and auto-
EM groundwave propagation is that a linear system of equations mates the application of Millington curve fitting method has
must be solved to yield currents induced on the ground scat- just been developed [10]. It becomes a very handy propagation
terers. The forward-backward method (FBM) is a stationary it- tool that can be used for everywhere for MF and HF bands
erative technique to overcome memory and computation burden instead of ITU-R P-368-7 curves.
SEVGI: GROUNDWAVE MODELING AND SIMULATION STRATEGIES AND PATH LOSS PREDICTION VIRTUAL TOOLS 1595

Fig. 4. The front panel of the Millington package and surface wave path loss
versus range over a 3-segment mixed path (sea-land-sea transition) due to a ver-
tically polarized short electric dipole on the surface, with the dipole moment
M = 5=2 [Am] at various frequencies. A 50-km long islands is located
at 75 km away from the source. Physical parameters: land,  = 0:003 [S=m],
Fig. 3. A 2-D multi mixed-path surface wave propagation scenario (d , i = " = 15; sea:  = 5: [S=m], " = 70.
; ; ; , represent the length of ith segment, S and r are total lengths from
1 2 3 ...
the transmitter and receiver, respectively up to the ith segment).

The mixed-path propagation scenario is pictured in Fig. 3(a).

The recursive equations of Millington curve fitting method [33]
described in [37] are

(17)

where and are the fields along direct (source-to-re-

ceiver) and reverse (receiver-to-source) paths, respectively. The
path lengths and Fig. 5. The Millington method versus European Frequency Management
Agency approach [52]: range variation of path loss along a 2-segment, 150-km
long mixed-path. The segment lengths are: d = 50 km, d = 100 km.
Electrical parameters: ( = 0:003 S=m, " = 15:0), ( = 5:0 S=m,
" = 70).

The application of Millington mixed-path method by using

ITU-R P-386-7 field strength curves is time consuming as
(18) mentioned above, therefore there are some other proposals for
this prediction problem. For example, the European Frequency
are as defined in Fig. 3(b). The total field along multi-mixed
Management Agency (EFMA) [52] advises to use
propagation path at the receiver is then obtained via the in-
terpolation of the direct and reverse electric fields as (19)
. The recursive equations reduce to
and for a 2-segment land-sea propagation path. The EFMA proposes
for a two-segment propagation path, where the (19) for the calculation of an undesired beacon at sea at a dis-
field values is the field strength at a distance over tance (where ), when the desired receiver
the th homogeneous medium. The effects of the number of is located on the land. Fig. 5 belongs to a comparison of the re-
multi-mixed paths, path-lengths, electrical parameters of each sults of ITU-R P-386-7 and the EFMA approaches. As observed
propagation section, as well as the frequency can be analyzed and verified in the figure for a 2-segment 150 km—long propa-
with this VT. In Fig. 4, the front panel of the VT and an gation scenario, this works for the frequencies below 500 kHz,
example of a three-section mixed-path scenario is given. Here, and with acceptable results up to 1–1.5 MHz. The error intro-
a 50-km long island at a distance of 75 km from the transmitter duced by using (19) in this frequency region will be less than a
is assumed. Electrical parameters of the sea and island are few (2–4) dB. The two results agree quite well at land-sea inter-
, and , , respec- section and over the sea path up to 5–10 km. It is obvious from
tively. As observed again, mixed-path problem is not important the figure that (19) can not be used for the frequencies above
for the frequencies below 500 kHz. 1.5 MHz.
1596 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 6, JUNE 2007

Fig. 6. The front panel of the GrSSPE, user specified terrain profile, Gaussian
source with specified vertical beamwidth and beam tilt. The 3-D field strength
versus range-height is plotted in the output window. The parameters are as sup- Fig. 7. The front panel of the GrFDTD and an instant of the pulse propagation
plied in the front panel. The example belongs to a typical tri-linear vertical re- along a user-specified terrain profile. Different colors correspond to different
fractivity profile that may cause surface as well as elevated ducts as observed. field strength values. Observe the line source emanating two short Gaussian-
shaped pulses, cylindrical wave spread and ground reflections.

B. Non-Flat Terrain and Atmospheric Refractivity Effects

uses the superposition of segment currents, and the total field
The most cited approaches in the groundwave propagation by the addition of the incident field.
modeling are the split-step parabolic equation method (widely The groundwave propagation methods mentioned in this sec-
known as PEM and SSPE), the MoM, and the FDTD. Figs. 6 to 9 tion have quite different mathematical models which are derived
belong to characteristic examples plotted via the virtual tools under different assumptions, approximations, have different ac-
designed using these three methods. curacy limits, and good for different parameter regimes. Except
The SSPE has been in use for many decades [19] and there the Millington method (which uses analytical ray-mode approx-
are excellent free PE-based propagation prediction tools (e.g., imations) they are all numerical models with different capabili-
AREPS in http://www.sunspot.spawar.navy.mil) which may be ties and validity ranges.
used for radar visibility analysis as well as tactical purposes and • The SSPE can handle forward scattered fields and edge-tip
decision aids. The SSPE is a one-way propagator that can handle diffracted fields (up to a certain extend), but neglects
non-flat (but smooth) terrain profiles as well as atmospheric backscattered field contributions. Its validity range is
refractivity variations. Although simplified and designed pri- limited with the paraxial region [19], therefore, the results
marily for educational purposes, the virtual tool GrSSPE (that may be erroneous in regions of longitudinal terrain profiles
was introduced recently [9]), is highly effective for the sim- with sharp upslopes and/or downslopes.
ulation of groundwave propagation problems. Any kind of a • The MoM can take two-way propagation effects into ac-
range-dependent non-flat terrain profile can be designed and count, but can not handle left and right termination (open
various refractivity profiles may be specified. As an example, boundary) conditions since it assumes that fields decay to
the propagation of an excited beam along this terrain through zero in these regions. Therefore, its results in the vicinity of
a tri-linear refractivity profile for the frequency of 100 MHz the source as well as the last ranges can not be reliable. Also,
is given in Fig. 6. The formation of both surface and elevated it can not handle diffracted fields in the shadow regions.
ducts (because of the refractivity variations) and terrain (for- • The FDTD can take both forward and backward propa-
ward)-scattered waves are clearly observed in the figure. gated waves as well as diffracted field contributions into
Fig. 7 belongs to another virtual tool GrFDTD [6] which uses account, but is restricted with the length of the sliding
a sliding window technique to cover propagation regions that window, so multi-reflections and diffractions can not be
are much larger than the numerical computation volume. The modeled in the present form.
propagation of both broad and narrow band (i.e., pulsed and si- Therefore, the most important issue in relation to the applica-
nusoidal) waves can be visualized in the TD with the GrFDTD. tion of groundwave propagators is their model validation, data
The example given in Fig. 7 shows a user-specified terrain pro- verification, and calibration. All these models have been already
file and line source emitting two consecutive Gaussian-shaped validated and verified in the literature therefore only a calibra-
pulses (an instant from the TD simulations). The cylindrical tion example and a few comparisons are included here. One
wave spread and reflections from the ground are clearly ob- should be careful in the choice of a test problem for the calibra-
served in the figure. tion; the 2-D flat-earth with the standard atmosphere is a canon-
The third package GrMoM [63] is a MoM-based virtual tool ical structure, has analytical exact solution, and serves as refer-
which requires the derivation of the 2-D analytical Green’s ence. The GrSSPE and GrMoM are FD tools, but the GrFDTD
function, fine discretization/segmentation of the user-specified is in the TD, therefore calibration should be done both in the
ground profile, the numerical solution of systems of linear TD and FD not only against the analytical exact solution, but
equations for the segment currents, calculation of the scattered also among them. The TD calibration requires multiple FD sim-
fields at the receiver in terms of the Green’s function which ulations for all resolution-adapted frequency samples spanning
SEVGI: GROUNDWAVE MODELING AND SIMULATION STRATEGIES AND PATH LOSS PREDICTION VIRTUAL TOOLS 1597

Fig. 8. The calibration of the GrMoM and GrSSPE VTs against the two-ray an-
alytical model over the flat Earth; (top) a 20-km flat propagation path at 10 MHz.
The transmitter and receiver heights are 300 m. The source is a line source, Fig. 9. Propagation factor versus range curves for two different non-flat propa-
(bottom) a 15-km path at 15 MHz. The transmitter and receiver heights are both gation scenarios; (top) a 20-km propagation path at 10 MHz. The transmitter is a
500 m above the ground. horizontal line source and is 400 m above the ground the receiver is 300 m above
the ground, (bottom) a 10-km propagation path at 15 MHz. The transmitter is
a vertical short dipole (TE -type problem) and is 300 m above the ground the
receiver is 10 m above the terrain.
the TD pulse spectrum, and the application of inverse Fourier
transform. The FD calibration necessitates time accumulation
of the short pulse propagation and the application of Fourier V. CONCLUSION
transform. Analytical and numerical groundwave propagation modeling
In Fig. 8, the results of MoM and SSPE are calibrated against and simulation studies conducted in collaboration with Leo
the exact solution of this idealized test scenario. The top figure Felsen and some of the virtual tools developed during this
shows the three curves for a 20 km propagation path at 10 MHz. period are reviewed in this paper. The beauty of the FD and
The transmitter and receiver heights are 300 m. The source is TD numerical propagators presented in this article resides in
a line source (i.e., it represents a -type 2-D problem). The the fact that they allow visualization, which is very important
field strength versus range curves obtained via the GrMoM in gaining physical insight for the problem at hand (as gained
and the GrSSPE virtual tools show very good agreement with from canonical problems through analytical formulations, such
the two-ray model. The bottom figure presents the propagation as ray and/or mode methods). As Leo always said, one should
factor versus range curves for a 15-km path at 15 MHz. The keep in mind the physics behind these numerical simulators in
transmitter and receiver heights are both 500 m which again order to use them efficiently and effectively.
shows a good agreement (note that some parameters of the
virtual tools are fixed to their average values to decrease their REFERENCES
run time, therefore slight discrepancies may occur as observed [1] L. B. Felsen and L. Sevgi, “Adiabatic and intrinsic modes for wave
in plots). propagation in guiding environments with longitudinal and transverse
variations: Formulation and canonical test,” IEEE Trans. Antennas
Although excellent agreement is obtained in the calibration Propag., vol. 39, no. 8, pp. 1130–1136, Aug. 1991.
tests, one has to be careful when using these models because of [2] L. B. Felsen and L. Sevgi, “Adiabatic and intrinsic modes for wave
their restricted capability and different validity ranges. In order propagation in guiding environments with longitudinal and transverse
variations: Continuously refracting media,” IEEE Trans. Antennas
to just give an idea, two example scenarios and calculations with Propag., vol. 39, no. 8, pp. 1137–1143, Aug. 1991.
the GrMoM and the GrSSPE are given in Fig. 9. The first sce- [3] L. Sevgi and L. B. Felsen, “A new algorithm for ground wave propaga-
tion based on a hybrid ray-mode approach,” Int. J. Numer. Modeling,
nario on top belongs to a 20 km propagation path at 10 MHz. vol. 11, no. 2, pp. 87–103, Ma. 1998.
The transmitter is a horizontal line source ( -type problem) [4] L. Sevgi, F. Akleman, and L. B. Felsen, “Ground wave propagation
and is 400 m above the ground while the receiver is 300 m above modelling: Problem-matched analytical formulations and direct nu-
merical techniques,” IEEE Antennas Propag. Mag., vol. 44, no. 1, pp.
the ground. The second scenario at bottom belongs to a 10 km 55–75, Feb. 2002.
propagation path at 15 MHz. The transmitter is a vertical short [5] L. B. Felsen, F. Akleman, and L. Sevgi, “Wave propagation inside
dipole ( -type problem) and is 300 m above the ground and a two-dimensional perfectly conducting parallel plate waveguide:
Hybrid ray-mode techniques and their visualisations,” IEEE Antennas
the receiver is 10 m above the terrain. The first and second sce- Propag. Mag., vol. 46, no. 6, pp. 69–89, Dec. 2004.
narios may be assumed as range recording of the signal on a [6] F. Akleman and L. Sevgi, “A novel finite difference time domain
wave propagator,” IEEE Trans. Antennas Propag., vol. 48, no. 5, pp.
plane flying at a constant altitude above the sea level and on a 839–841, May 2000.
trunk, respectively. All curves show propagation factor versus [7] M. O. Ozyalcin, F. Akleman, and L. Sevgi, “A novel TLM based time
range variations. It is a real challenge to the propagation engi- domain wave propagator,” IEEE Trans. Antennas Propag., vol. 51, no.
7, pp. 1679–1683, Jul. 2003.
neer to comment on the results, and requires a good knowledge [8] L. Sevgi, Complex Electromagnetic Problems and Numerical Simula-
of physics as well as experience. tion Approaches. Piscataway, NJ: IEEE Press/Wiley, Jun. 2003.
1598 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 6, JUNE 2007

[9] L. Sevgi, Ç. Uluışık, and F. Akleman, “A Matlab-based two-dimen- [39] ITU-R, Recommendations, BS-1615, Planning Parameter for Digital
sional parabolic equation radiowave propagation package,” IEEE An- Sound Broadcasting at Frequencies Below 30 MHz International
tennas Propag. Mag., vol. 47, no. 4, pp. 184–195, Aug. 2005. Telecommunications Union, 2003.
[10] L. Sevgi, “A mixed-path groundwave field strength prediction virtual [40] F. R. Dinapoli and R. L. Deavenport, Numerical Methods of Under-
tool for digital radio broadcast systems in medium and short wave water Acoustic Propagation, J. A. Desanto, Ed. New York: Springer
bands,” IEEE Antennas Propag. Mag., vol. 48, no. 4, pp. 19–27, Aug. Verlag, 1977.
2006. [41] M. D. Collins, “A split-step Padé solution for the parabolic equation
[11] L. Sevgi, “Virtual tools/labs in electrical engineering education,” method,” J. Acoust. Soc. Amer., vol. 94, pp. 1736–1742, 1993.
ELEKTRIK, Turkish J. of Elect. Eng. Comput. Sci. (Special Issue on [42] M. F. Levy, “Horizontal parabolic equation solution of radio wave
Electrical and Computer Engineering Education in the 21st Century: propagation problems on large domains,” IEEE Trans. Antennas
Issues, Perspectives and Challenges), vol. 14, no. 1, pp. 113–127, Propag., vol. 43, no. 2, pp. 137–144, 1995.
2006. [43] G. D. Dockery and J. R. Kuttler, “An improved impedance boundary
[12] L. B. Felsen and L. Sevgi, “Electromagnetic engineering in the 21st algorithm for Fourier split-step solutions of the parabolic wave equa-
century: Challenges and perspectives,” Special Issue of ELEKTRIK, tion,” IEEE Trans. Antennas Propag., vol. 44, no. 12, pp. 1592–1599,
Turkish J. Elect. Eng. Comput. Sci., vol. 10, no. 2, pp. 131–145, Feb. 1996.
2002, (introductory paper). [44] G. D. Dockery, “Modelling electromagnetic wave propagation in the
[13] J. R. Wait, Electromagnetic Waves in Stratified Media. Oxford: Perg- troposphere using parabolic wave equation,” IEEE Trans. Antennas
amon, 1962. Propag., vol. 36, pp. 1464–1470, 1988.
[14] V. A. Fock, Electromagnetic Diffraction and Propagation Problems. [45] A. E. Barrios, “Parabolic equation modelling in horizontally inhomo-
Oxford, U.K.: Pergamon, 1965, pp. 191, 235. geneous environments,” IEEE Trans. Antennas Propag., vol. 40, pp.
[15] D. E. Kerr, Ed., The Propagation of Short Radio Waves, ser. Radiation 791–797, 1992.
Lab. Series. New York: McGraw Hill, 1951, vol. 13. [46] A. E. Barrios, “A terrain parabolic equation model for propagation in
[16] M. P. M. Hall, L. W. Barclay, and M. T. Hewitt, Eds., Propagation of the troposphere,” IEEE Trans. Antennas Propag., vol. 42, pp. 90–98,
Radiowaves. London, U.K.: IEE Press, 1996. 1994.
[17] W. C. L. Yee, Mobile Cellular Telecommunication Systems. New [47] D. J. Donohue and J. R. Kuttler, “Propagation modeling over terrain
York: McGraw-Hill, 1989. using the parabolic wave equation,” IEEE Trans. Antennas Propag.,
[18] H. Bertoni, Radio Propagation for Modern Wireless Systems. Engle- vol. 48, no. 2, pp. 260–277, Feb. 2000.
wood Cliffs, NJ: Prentice Hall, 2000. [48] A. D. Thomson and T. D. Quach, “Application of PE methods to prop-
[19] M. Levy, Parabolic Equation Methods for Electromagnetic Wave Prop- agation in an arctic environment,” IEEE Trans. Antennas Propag., vol.
agation. London, U.K.: Institution of Electrical Engineers, 2000. 4, no. 1, pp. 412–419, Jan. 2005, Vo. 53.
[20] R. F. Harrington, Field Computation by Moment Method. New York: [49] A. A. Zaporozhets, “Application of vector parabolic equation method to
IEEE Press, 1993. urban radiowave propagation problems,” Proc. Inst. Elect. Eng.—Mi-
[21] “Special issue on low-grazing-angle backscattering from rough sur- crow, Antennas Propag., vol. 146, no. 4, Aug. 1999.
faces,” IEEE Trans. Antennas Propag., vol. 46, Jan. 1998. [50] R. Janaswamy, “Path loss predictions in the presence of buildings on
[22] C. A. Tunc, A. Altintas, and V. B. Erturk, “Examination of existent flat terrain: A 3-D vector parabolic equation approach,” IEEE Trans.
propagation models over large inhomogeneous terrain profiles using Antennas Propag., vol. 51, no. 8, pp. 1716–1728, Aug. 2003.
fast integral equation solution,” IEEE Trans. Antennas Propag., vol. [51] F. Akleman, M. O. Özyalçin, and L. Sevgi, “Novel time domain wave
53, no. 9, pp. 3080–3083, Sep. 2005. propagators for wireless communication systems,” Special Issue of
[23] F. Akleman and L. Sevgi, “Realistic surface modeling in a time-domain ELEKTRIK, Turkish J. Elect. Eng. Comput. Sci., vol. 10, no. 2, pp.
wave propagator,” IEEE Trans. Antennas Propag., vol. 51, no. 7, pp. 198–216, Feb. 2002.
1675–1679, Jul. 2003. [52] “European Frequency Management Manual” 2005 [Online]. Avail-
[24] B. Fidel, E. Heyman, R. Kastner, and R. W. Ziolkowski, “A hybrid able: http://www.eu.int, ICAO EUR Doc 011
ray-FDTD moving frame approach to pulse propagation,” J. Comput. [53] Ç. Uluışık and L. Sevgi, “Numerical modeling and simulation studies
Phys., vol. 138, no. 2, pp. 480–500, 1997. of 2-D radiowave propagation over non-flat terrain and through inho-
[25] N. De Minco, “Propagation prediction techniques and antenna mod- mogeneous atmosphere,” Complex Computing Networks, ser. Springer
eling (150 to 1705 kHz) for Intelligent Transportation Systems (ITS) Proceedings in Physics Series, vol. 104, pp. 45–54, Jan. 2006.
broadcast applications,” IEEE Trans. Antennas Propag. Mag., vol. 42,
no. 4, pp. 9–33, Aug. 2000.
[26] A. D. Pierce, “Extension of the method of normal modes to sound prop-
agation in almost stratified medium,” J. Acoust. Soc. Amer., vol. 37, pp. Levent Sevgi (M’00–SM’02) received the B.S.E.E.,
19–27, 1965. M.S.E.E., and Ph.D. degrees in electronic engi-
[27] J. M. Arnold and L. B. Felsen, “Intrinsic modes in a wedge shaped neering from Istanbul Technical University (ITU),
ocean,” J. Acoust. Soc. Amer., vol. 76, pp. 850–860, 1984. Istanbul, Turkey, in 1982, 1984, and 1990, respec-
[28] E. Topuz and L. B. Felsen, “Intrinsic modes: Numerical implemen- tively.
tation in a wedge-shaped ocean,” J. Acoust. Soc. Amer., vol. 88, pp. In 1982, he joined the Electrical Faculty of ITU as
1735–1745, 1985. a Research Assistant. In 1987, while working on his
[29] J. C. Schelleng, C. R. Burrows, and E. B. Ferrel, “Ultra-short wave Ph.D. he was awarded a fellowship that allowed him
propagation,” Proc. IRE, vol. 21, pp. 427–463, March 1933. to work with Prof. L. B. Felsen at Weber Research
[30] J. Deygout, “Multiple knife-edge diffraction of microwaves,” IEEE Institute/New York Polytechnic University York for
Trans. Antennas Propag., vol. 51, no. 7, pp. 1679–1683, Jul. 1966. two years. His work at the Polytechnic concerned the
[31] K. A. Norton, “The propagation of radio waves over the surface of earth propagation phenomena in nonhomogeneous open and closed waveguides. He
and in the upper atmosphere,” Proc. IRE, vol. 24, pp. 1367–1387, 1936. was with the Center for Defense Studies, ITUV-SAM, from 1993 to 2001. He
[32] J. R. Wait, “On the theory of mixed-path ground-wave propagation on spent nearly a year with the Scientific Research Group of Raytheon Systems
a spherical earth,” J. Research NBS, vol. 65D, pp. 401–410, 1961. Canada from September 1998 until June 1999, during the field trials of the Cana-
[33] G. Millington, “Ground wave propagation over an inhomogeneous dian East Coast Integrated Maritime Surveillance System based on surface wave
smooth earth,” Proc. IRE, vol. 96, no. 39, pp. 53–64, 1949. HF Radars. He joined the Information Technologies Research Institute of the
[34] J. R. Wait and L. C. Walters, “Curves for ground wave propagation Turkish Scientific Research and Technology Council (TUBITAK-MRC) as the
over mixed land sea paths,” IEEE Trans. Antennas Propag., vol. 11,
Chair of Electronic Systems Department in June 1999 and spent nearly two years
pp. 38–45, 1963.
there . Since February 2002, he has been a member of the Engineering Faculty in
[35] D. A. Hill and J. R. Wait, “HF ground wave propagation over mixed
land, sea, sea-ice paths,” IEEE Trans. Geosci. Remote Sensing, vol. 19, the Electronics and Communication Engineering Department at Doğuş Univer-
pp. 210–216, 1981. sity in Kadikoy-Istanbul. He is the author or coauthor of nearly 150 journal and
[36] CCIR, Ground Wave Propagation Curves for Frequencies Between 10 conference papers, a few book chapters and an IEEE Press book. His research
kHz and 30 MHz CCIR Rec. 368-6, 1990. study has focused on propagation in complex environments, analytical and nu-
[37] ITU-R, Recommendations, P-368-7, Groundwave Propagation Curves merical methods in electromagnetics and radar systems, EMC/EMI modeling
for Frequencies Between 10 kHz and 30 MHz International Telecom- and measurement, surface wave HF radars, FDTD, TLM, SSPE and MoM tech-
munications Union, Mar. 1992. niques and their applications, RCS modeling, and bioelectromagnetics. He is
[38] ITU-R, Recommendations, P-1321, Propagation Factors Affecting also interested in novel approaches in engineering education, teaching electro-
Systems Using Digital Modulation Techniques at LF and MF Interna- magnetics via virtual tools. Recently, he started to teach popular science lectures
tional Telecommunications Union, Aug. 1997. like Science, Technology and Society.